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Block #364,309

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2014, 11:35:34 PM Β· Difficulty 10.4224 Β· 6,437,238 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
2b272b5cf183d31a251cdaed1be7bed07e6b4e2b505d9d0a119401596eee7059
View on Chainz β†—

Height

#364,309

Difficulty

10.422439

Transactions

1

Size

207 B

Version

2

Bits

0a6c24f4

Nonce

29,483

Timestamp

1/17/2014, 11:35:34 PM

Confirmations

6,437,238

Merkle Root

dc3440b2b7f1e177d78d521b8887db5f5b49808cfdb62e945166b2d219be22f6
Transactions (1)
Coinbasedc3440b2b7f1e1…66b2d219be22f6
1 in β†’ 1 out9.1900 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.044 Γ— 10⁹⁸(99-digit number)
10442863931650010643…09908539693802959680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.044 Γ— 10⁹⁸(99-digit number)
10442863931650010643…09908539693802959679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁸(99-digit number)
20885727863300021287…19817079387605919359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.177 Γ— 10⁹⁸(99-digit number)
41771455726600042574…39634158775211838719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.354 Γ— 10⁹⁸(99-digit number)
83542911453200085148…79268317550423677439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁹(100-digit number)
16708582290640017029…58536635100847354879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.341 Γ— 10⁹⁹(100-digit number)
33417164581280034059…17073270201694709759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.683 Γ— 10⁹⁹(100-digit number)
66834329162560068118…34146540403389419519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.336 Γ— 10¹⁰⁰(101-digit number)
13366865832512013623…68293080806778839039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.673 Γ— 10¹⁰⁰(101-digit number)
26733731665024027247…36586161613557678079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.346 Γ— 10¹⁰⁰(101-digit number)
53467463330048054494…73172323227115356159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 364309

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 2b272b5cf183d31a251cdaed1be7bed07e6b4e2b505d9d0a119401596eee7059

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #364,309 on Chainz β†—
Circulating Supply:57,656,456 XPMΒ·at block #6,801,546 Β· updates every 60s
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